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Mirabolic Howe Duality
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DOI：10.1007/s11464-025-0150-9.png)
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Abstract
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We introduce the space MVn|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{MV}_{n|m}$$\end{document} as the space of G-invariant functions on the variety of triples of two partial flag varieties and a vector space. Subsequently, we define the action of the mirabolic quantum Schur algebra via convolution multiplication. Finally, we present the geometric approach of the mirabolic Howe duality.
Keywords:
Howe duality
mirabolic quantum groups
flag variety
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0.4
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42
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